Question: $f(n) = -n^{3}-5n^{2}-3n-2(h(n))$ $h(x) = -5x^{2}+2x+5$ $g(x) = 2x^{2}-5(h(x))$ $ f(h(-1)) = {?} $
First, let's solve for the value of the inner function, $h(-1)$ . Then we'll know what to plug into the outer function. $h(-1) = -5(-1)^{2}+(2)(-1)+5$ $h(-1) = -2$ Now we know that $h(-1) = -2$ . Let's solve for $f(h(-1))$ , which is $f(-2)$ $f(-2) = -(-2)^{3}-5(-2)^{2}+(-3)(-2)-2(h(-2))$ To solve for the value of $f$ , we need to solve for the value of $h(-2)$ $h(-2) = -5(-2)^{2}+(2)(-2)+5$ $h(-2) = -19$ That means $f(-2) = -(-2)^{3}-5(-2)^{2}+(-3)(-2)+(-2)(-19)$ $f(-2) = 32$